【Theory webinar】Rank-preserving Multidimensional Mechanisms

  • 研討會日期 : 2021-10-05
  • 時間 : 14:30
  • 主講人 : Professor Debasis Mishra
  • 主持人 : Professor Ritesh Jain
  • 地點 : online or Conference Room B110
  • 演講者簡介 : Professor Mishra received his Ph.D. in Industrial Engineering from University of Wisconsin, Madison in 2004. He is currently a Professor at Indian Statistical Institute, New Delhi. His research interests are theory of auctions and mechanism design, social choice theory, game theory.
  • 演講摘要 : We study the mechanism design problem of a monopolist with multiple heterogeneous indivisible objects. The buyer’s type is multidimensional, with a value for each object. The value for a bundle of objects is the sum of the value of each object in the bundle. We introduce a new property which we call rank preserving. A mechanism is rank preserving if objects with greater buyer values are allocated with (weakly) higher probabilities. We show that in an exchangeable environment (i.e., type space is a n-dimensional cube and the prior is symmetric), there exists an optimal (i.e., revenue maximizing) mechanism which is rank preserving and symmetric. However, an optimal deterministic mechanism need not be symmetric or rank preserving. We show that an optimal deterministic mechanism that is symmetric exists if and only if an optimal deterministic mechanism that is rank preserving exists. If a mechanism satisfies aggregate monotonicity, i.e., the sum of all tail allocation probabilities increases as the value of an object increases, then the mechanism is revenue monotone (i.e., higher types pay more). As an application of this result, we show that an almost deterministic mechanism is revenue monotone. We establish an equivalence between symmetric, rank-preserving mechanisms in this heterogeneous objects model and mechanisms for homogeneous objects with decreasing marginal values.